The invention is related to the field of quantum sensors and quantum dynamic parameter estimation, and in particular to time-resolved magnetic sensing with electronic spins in diamond.
Precision measurement is among the most important applications of quantum physics. For example, quantum control of atomic systems forms the physical basis of the world's best clocks. The purpose of quantum metrology is to detect a small external field, coupled to the sensor by a Hamiltonian: HbS=b(t)κSz, where Sz is the spin operator of the quantum sensor. Here, b(t) can be an external magnetic field or the detuning of a laser from a clock transition while κ is the spin's coupling to the field.
The working principle of almost any quantum metrology scheme can be reduced to a Ramsey experiment, where the field is measured via the induced phase difference between two states of the quantum sensor. The quantum probe is prepared in a superposition of two eigenstates of the operator Sz, e.g.
              ψ      ⁡              (        0        )              =                  1        2            ⁢              (                                          0            〉                    +                                  1            〉                          )              〉and is then let evolve freely under the action of the external field. The eigenstates acquire a phase that is proportional to their eigenvalues (here 0 and 1) and to the parameter to be estimated:
                        ψ        ⁡                  (          τ          )                    =                        1          2                ⁢                  (                                                  0              〉                        +                                          ⅇ                                  ⅈφ                  ⁡                                      (                    τ                    )                                                              ⁢                                              1                〉                                              )                      〉    ,with φ(τ)=κ∫0T b(t)dt. This phase difference can be converted in a population difference and measured out. The figure of merit for quantum sensitivity is the smallest field Υbmin that can be read out during a total time T. For a single spin ½, if the sensing time is limited to τ (e.g. by environmental decoherence) then:
      δ    ⁢                  ⁢          b      min        ≈            1              κ        ⁢                              T            ⁢                                                  ⁢            τ                                .  